Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Dynamics of a reaction-diffusion system of autocatalytic chemical reaction

Pages: 245 - 258, Volume 21, Issue 1, May 2008      doi:10.3934/dcds.2008.21.245

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Jifa Jiang - Department of Mathematics, Tongji University, Shanghai 200092, China (email)
Junping Shi - Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187, United States (email)

Abstract: The precise dynamics of a reaction-diffusion model of autocatalytic chemical reaction is described. It is shown that exactly either one, two, or three steady states exists, and the solution of dynamical problem always approaches to one of steady states in the long run. Moreover it is shown that a global codimension one manifold separates the basins of attraction of the two stable steady states. Analytic ingredients include exact multiplicity of semilinear elliptic equation, the theory of monotone dynamical systems and the theory of asymptotically autonomous dynamical systems.

Keywords:  autocatalytic chemical reaction, asymptotic autonomous system, convergence to equilibrium.
Mathematics Subject Classification:  Primary: 35J55; Secondary: 35B40, 80A32.

Received: January 2007;      Revised: May 2007;      Available Online: February 2008.